From the course: Complete Guide to Calculus Foundations for Data Science
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Sum and difference rules
From the course: Complete Guide to Calculus Foundations for Data Science
Sum and difference rules
- [Instructor] Next, let's explore the sum and difference rules for integrals. These rules are essentially one and the same, but they're sometimes referenced separately. It is important to know how both of these rules work since they can be extremely helpful when solving integrals. Note that these also function similarly to their derivative counterparts. Let's begin with the sum rule. The sum rule states the integral of a sum of functions is the same as the sum of their integrals. This is represented by the functions H of X equal to the function F of X, added, with the function G of X. The integral of the function H of X is equal to the integral of H of X DX, equals the integral of F of X DX, plus the integral of G of X DX. Next is the difference rule. The difference rule states the integral of a difference of functions is the same as the difference of their integrals. This is represented by the functions H of X is equal to the function of F of X minus the function of G of X, where…
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